Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:

import java.util.Scanner;

public class FunkyNumber {

    public static void main(String[] args) {
        Scanner inp = new Scanner(System.in);
        int n = inp.nextInt();
        for (long i = 1; i < Math.sqrt(n) + 1; i++) {
            if (sol(1, -1, (i + 1) * i - 2 * n) > 1) {
                System.out.println("YES");
                //long s = sol(1, -1, (i+1)*i-2*n)-1;
                //System.out.println(i+","+s+","+gettingN(i, s));
                return;
            }
        }
        System.out.println("NO");
    }

    static long sol(int a, int b, long c) {
        double x1 = -b + Math.sqrt(b * b - 4 * a * c);
        if (Math.ceil(x1) == x1) {
            return (long) x1 / 2;
        } else {
            return 0;
        }

    }
//   static long gettingN(long k, long m) {
//        return (k * (k + 1) + m * (m + 1)) / 2;
//    }
}